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A Bayesian model and numerical algorithm for CBM availability maximization

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  • Rui Jiang
  • Michael Kim
  • Viliam Makis

Abstract

In this paper, we consider an availability maximization problem for a partially observable system subject to random failure. System deterioration is described by a hidden, continuous-time homogeneous Markov process. While the system is operational, multivariate observations that are stochastically related to the system state are sampled through condition monitoring at discrete time points. The objective is to design an optimal multivariate Bayesian control chart that maximizes the long-run expected average availability per unit time. We have developed an efficient computational algorithm in the semi-Markov decision process (SMDP) framework and showed that the availability maximization problem is equivalent to solving a parameterized system of linear equations. A numerical example is presented to illustrate the effectiveness of our approach, and a comparison with the traditional age-based replacement policy is also provided. Copyright Springer Science+Business Media, LLC 2012

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  • Rui Jiang & Michael Kim & Viliam Makis, 2012. "A Bayesian model and numerical algorithm for CBM availability maximization," Annals of Operations Research, Springer, vol. 196(1), pages 333-348, July.
    • Handle: RePEc:spr:annopr:v:196:y:2012:i:1:p:333-348:10.1007/s10479-011-1013-1
    DOI: 10.1007/s10479-011-1013-1
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    References listed on IDEAS

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    1. Joel M. Calabrese, 1995. "Bayesian Process Control for Attributes," Management Science, INFORMS, vol. 41(4), pages 637-645, April.
    2. V. Makis & X. Jiang, 2003. "Optimal Replacement Under Partial Observations," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 382-394, May.
    3. Wu, Jianmou & Makis, Viliam, 2008. "Economic and economic-statistical design of a chi-square chart for CBM," European Journal of Operational Research, Elsevier, vol. 188(2), pages 516-529, July.
    4. Sheu, Shey-Huei & Griffith, William S., 2002. "Extended block replacement policy with shock models and used items," European Journal of Operational Research, Elsevier, vol. 140(1), pages 50-60, July.
    5. Richard Barlow & Larry Hunter, 1960. "Optimum Preventive Maintenance Policies," Operations Research, INFORMS, vol. 8(1), pages 90-100, February.
    6. Christer, A. H. & Wang, W. & Sharp, J. M., 1997. "A state space condition monitoring model for furnace erosion prediction and replacement," European Journal of Operational Research, Elsevier, vol. 101(1), pages 1-14, August.
    7. Taylor, R. W., 1996. "A linear programming model to manage the maintenance backlog," Omega, Elsevier, vol. 24(2), pages 217-227, April.
    8. Sarkar, Jyotirmoy & Chaudhuri, Gopal, 1999. "Availability of a system with gamma life and exponential repair time under a perfect repair policy," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 189-196, June.
    9. Chen, Dongyan & Trivedi, Kishor S., 2005. "Optimization for condition-based maintenance with semi-Markov decision process," Reliability Engineering and System Safety, Elsevier, vol. 90(1), pages 25-29.
    10. Serge Provost & Edmund Rudiuk, 1996. "The exact distribution of indefinite quadratic forms in noncentral normal vectors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(2), pages 381-394, June.
    11. Nenes, George & Tagaras, George, 2007. "The economically designed two-sided Bayesian control chart," European Journal of Operational Research, Elsevier, vol. 183(1), pages 263-277, November.
    12. Biswas, Atanu & Sarkar, Jyotirmoy, 2000. "Availability of a system maintained through several imperfect repairs before a replacement or a perfect repair," Statistics & Probability Letters, Elsevier, vol. 50(2), pages 105-114, November.
    13. Kim, Michael Jong & Makis, Viliam & Jiang, Rui, 2010. "Parameter estimation in a condition-based maintenance model," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1633-1639, November.
    14. Makis, Viliam, 2009. "Multivariate Bayesian process control for a finite production run," European Journal of Operational Research, Elsevier, vol. 194(3), pages 795-806, May.
    15. Bertolini, Massimo & Bevilacqua, Maurizio, 2006. "A combined goal programming—AHP approach to maintenance selection problem," Reliability Engineering and System Safety, Elsevier, vol. 91(7), pages 839-848.
    16. Viliam Makis, 2008. "Multivariate Bayesian Control Chart," Operations Research, INFORMS, vol. 56(2), pages 487-496, April.
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    Cited by:

    1. Naderkhani, Farnoosh & Makis, Viliam, 2016. "Economic design of multivariate Bayesian control chart with two sampling intervals," International Journal of Production Economics, Elsevier, vol. 174(C), pages 29-42.
    2. Zhang, Nan & Cai, Kaiquan & Deng, Yingjun & Zhang, Jun, 2024. "Joint optimization of condition-based maintenance and condition-based production of a single equipment considering random yield and maintenance delay," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    3. Nooshin Salari & Viliam Makis, 2020. "Joint maintenance and just-in-time spare parts provisioning policy for a multi-unit production system," Annals of Operations Research, Springer, vol. 287(1), pages 351-377, April.
    4. Lirong Cui & Shijia Du & Aofu Zhang, 2014. "Reliability measures for two-part partition of states for aggregated Markov repairable systems," Annals of Operations Research, Springer, vol. 212(1), pages 93-114, January.
    5. Zhang, Nan & Cai, Kaiquan & Deng, Yingjun & Zhang, Jun, 2023. "Determining the optimal production–maintenance policy of a parallel production system with stochastically interacted yield and deterioration," Reliability Engineering and System Safety, Elsevier, vol. 237(C).
    6. Reza Ahmadi, 2014. "Optimal maintenance scheduling for a complex manufacturing system subject to deterioration," Annals of Operations Research, Springer, vol. 217(1), pages 1-29, June.

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